IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v87y2025i1d10.1007_s13171-024-00364-8.html
   My bibliography  Save this article

A General Formulation for the Large-Sample Behaviour of a Class of Hypothesis Test Statistics

Author

Listed:
  • Ross Maller

    (Australian National University)

  • Maryam Ghodsi

    (Islamic Azad University)

Abstract

We bring together some strands of development concerning restricted likelihood ratio estimation and testing, including boundary hypothesis testing, going back to pioneering papers of Aitchison, Silvey and Chernoff for motivation. Thus, cases where the parameters are connected by a number of functional relationships, which may involve natural restrictions on the parameters and/or restrictions imposed by a null hypothesis, as well as situations where the null and alternate hypotheses place the true parameter at the boundary of disjoint subsets of the parameter space, are considered. Our asymptotic results are proved under clearly specified and minimal assumptions, which are probably close to the weakest possible. We illustrate with an example for distributions defined on the unit sphere in $$\mathbb {R}^{\varvec{d}}$$ R d .

Suggested Citation

  • Ross Maller & Maryam Ghodsi, 2025. "A General Formulation for the Large-Sample Behaviour of a Class of Hypothesis Test Statistics," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(1), pages 1-40, February.
    • Handle: RePEc:spr:sankha:v:87:y:2025:i:1:d:10.1007_s13171-024-00364-8
    DOI: 10.1007/s13171-024-00364-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-024-00364-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-024-00364-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
    2. R. M. Kuiper & H. Hoijtink & M. J. Silvapulle, 2011. "An Akaike-type information criterion for model selection under inequality constraints," Biometrika, Biometrika Trust, vol. 98(2), pages 495-501.
    3. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    4. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    5. H. Vu & R. Maller & X. Zhou, 1998. "Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 627-653, December.
    6. Vu, H. T. V. & Maller, R. A. & Klass, M. J., 1996. "On the Studentisation of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 142-155, April.
    7. Watson, Geoffrey S., 1984. "The theory of concentrated Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 74-82, February.
    8. Claudia Klüppelberg & Ross A. Maller & Mark van de Vyver & Derick Wee, 2002. "Testing for reduction to random walk in autoregressive conditional heteroskedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 387-416, June.
    9. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    10. Grömping, Ulrike, 2010. "Inference with Linear Equality and Inequality Constraints Using R: The Package ic.infer," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i10).
    11. Maller, R. A., 2003. "Asymptotics of regressions with stationary and nonstationary residuals," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 33-67, May.
    12. Trevor S. Breusch, 1986. "Hypothesis Testing in Unidentified Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 635-651.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
    3. Dustmann C. & Van Soest A., 2004. "An Analysis of Speaking Fluency of Immigrants Using Ordered Response Models With Classification Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 312-321, July.
    4. Timo Dimitriadis & iaochun Liu & Julie Schnaitmann, 2023. "Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 412-444.
    5. Ekaterina Oparina & Sorawoot Srisuma, 2022. "Analyzing Subjective Well-Being Data with Misclassification," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 730-743, April.
    6. Hanming Fang & Yang Wang, 2015. "Estimating Dynamic Discrete Choice Models With Hyperbolic Discounting, With An Application To Mammography Decisions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(2), pages 565-596, May.
    7. Zhu, Hongtu & Zhang, Heping, 2006. "Asymptotics for estimation and testing procedures under loss of identifiability," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 19-45, January.
    8. Ben, Youhong & Jiang, Feiyu, 2020. "A note on Portmanteau tests for conditional heteroscedastistic models," Economics Letters, Elsevier, vol. 192(C).
    9. Samuele Centorrino & María Pérez‐Urdiales & Boris Bravo‐Ureta & Alan Wall, 2024. "Binary endogenous treatment in stochastic frontier models with an application to soil conservation in El Salvador," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 365-382, April.
    10. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    11. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    12. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    13. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    14. LaFrance, Jeffrey T., 2008. "The structure of US food demand," Journal of Econometrics, Elsevier, vol. 147(2), pages 336-349, December.
    15. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    16. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "Applications of subsampling, hybrid, and size-correction methods," Journal of Econometrics, Elsevier, vol. 158(2), pages 285-305, October.
    17. Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2019. "Testing Garch-X Type Models," Econometric Theory, Cambridge University Press, vol. 35(5), pages 1012-1047, October.
    18. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    19. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    20. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2017. "On the Consistency of Bootstrap Testing for a Parameter on the Boundary of the Parameter Space," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 513-534, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:87:y:2025:i:1:d:10.1007_s13171-024-00364-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.